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THE FEUTEX TOOLKIT

Chebyshev Coverage Guarantee

Bound the fraction outside a selected distance from the mean using only finite variance.

Probability workspace● Runs in your browser
01 Your input
02 Your result
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FormulaOutside Upper = min(1,sd**2/distance**2); Inside Lower = max(0,1-sd**2/distance**2)
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Made for real tasks

  • Bound the fraction outside a selected distance from the mean using only finite variance.
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Worked example

Inputs

Population standard deviation
2 number
Absolute distance from mean
6 number

Expected results

Outside Upper
0.1111111111 probability
Inside Lower
0.8888888889 probability

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter population standard deviation, absolute distance from mean.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "sd": 2,
  "distance": 6
}

Accuracy and scope

Distribution-free bound, usually conservative; requires a true finite population variance, not automatically a reliable sample estimate.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.